Exclusions have to be sanctioned by the Head, so that's the person to speak to. It's usually mandatory for 'fighting'. A really nice lass in my Y9 form was excluded years ago. Put a bully on her back, same as your lad. I offered to speak to her Dad, but he was totally supportive of his daughter, so no need. Spoke to the HOY, and he told me he didn't have an option.
As BRB said, if he was in uniform it's a school matter. 5 days was excessive though. 2 days would have been fairer.
Get onto the little lad's parents. Get 'em to kick up a stink about the bully.